1. Supergranule Scale Convection Simulations
Robert Stein, David Benson, Dali Georgobiani
Michigan State University, USA
Aake Nordlund, Copenhagen University, DK

2. Supergranulation Simulation 48 Mm wide x 20 Mm deep
65 hours (1.3 turnover time)
f-plane rotation (surface shear layer)
No magnetic field (yet)
Low resolution:
100 km horizontal,
12-70 km vertical

3. Mean Atmosphere Temperature, Density and Pressure (K) (105 dynes/cm2)
(10-7 gm/cm2)

4. Mean Atmosphere
Ionization of He, He I and He II

5. Surface Shear Layer f-plane rotation
latitude of 30 degrees
imposed rotation through the coriolis force --- not an imposed profile
+/- signs --- directions ????
plot is an hour average --- after how long? -- recent ---> just beginning to study this
significant fluctuations -- particularly near the surface
extent is larger than observed --- likely due to the viscous flux in the numerical viscosity

6. Velocity in vertical plane
hr sequence (out of 50 hrs).
single slice -- 48Mm by 20 Mm deep
downflows merge and swept to sides by the diverging upflows
some are merging -- some are getting halted by colliding with upflows
in total ---> 46 hours solar -- 1 turnover time --- here 6 hours

7. vertical velocity on horizontal planes (48 Mm wide)
l to r --> top to bottom
surface, 2, 4, 8, 12, 16 Mm
scale of features gradually (continually) gets larger with depth
note: bottom has not relaxed yet
no special thing for mesogranulation -- no special thing for supergranulation -- why so apparent is still not clear
l to r --> top to bottom :: surface, 2Mm, 4Mm, 8Mm, 12Mm, 16Mm
Continuous scale change: granulates -> supergranules

8. Scan of temperature with depth

9. Time evolution at various depths

10. How to calculate the spectrum?
Average power spectra (correct) or Average time sequence (incorrect)
Noisy
Artificial feature,

11. P-mode power (red), convective power (black) – time average (blue)
Note that it matters very much for smoothness how one computes power spectra
Hi-res MDI

12. Velocity spectrum only distinct scale is granulation
convection
Vhoriz (sim)
…. oscillations
Vz(sim)
V MDI

13. Horizontal Velocity Spectrum
-200 km
0 Mm
2 Mm
4 Mm
8 Mm
16 Mm

14. Upflows at surface come from small area at bottom (left) Downflows at surface converge to supergranule boundaries (right)
seeded at regular intervals at bottom Mm intervals
upflows -- most turns over before it gets to the surface
most of the upflows diverging -- see them coming back down at the edges of the supergranules
color -- just shading -- yellow at bottom and red at top
catch basin for the downflows
merging of downflows
thanks to Chris Henze at NASA Ames

15. Stream lines seeded at bottom

16. Wave propagation
Courtesy Junwei Zhao

17. k-w Diagram
simulation
MDI

18. Time-Distance Inversions Depth 1-2 Mm
Simulation
Inversion
Time-Distance Inversions Depth 1-2 Mm

19. Time-Distance Inversions Depth 2-3 Mm
Simulation
Inversion
Time-Distance Inversions Depth 2-3 Mm

20. Time-Distance Inversions Depth 4-5 Mm
Simulation
Inversion
Time-Distance Inversions Depth 4-5 Mm

21. Initialization Snapshot
Doubled + Stretched = bootstraped initial state
Snapshots of methods + composite (?)